When the function \(W\)  is locally Lipschitz continuous on \(\Omega \) , the limiting subdifferential \(\partial _LW(x)\)  is nonempty at every point, the set-valued map \(x\rightsquigarrow \partial _LW(x)\)  is upper semicontinuous, and the Clarke generalized gradient at \(x\)  can be derived as co \(\partial _LW(x)\) . As sources for nonsmooth analysis we refer e.g. to [1]}, [2]}, [3]}.
